Situation-dependent observation errors for AMSU-A
tropospheric channels in the ECMWF forecasting system
Heather Lawrence, Niels Bormann, Enza Di Tomaso and Stephen English
ECMWF, Shinfield Park, Reading
RG2 9AX, United Kingdom
heather.lawrence@ecmwf.int
ABSTRACT
The Advanced Microwave Sounding Unit-A (AMSU-A) is a key satellite instrument used in numerical weather
prediction systems around the world. In order to assimilate AMSU-A data, observation errors must be defined.
In the ECMWF system each AMSU-A channel is currently assigned a constant observation error. However the
observation errors should include forward model error, which will depend on the state of the atmosphere and
surface. Here we present a study where observation errors for the surface- and cloud-sensitive channels were
allowed to vary with surface type (land, sea, sea-ice, snow cover), sensitivity to the surface (surface-to-space
transmittance) and the liquid water path, in order to account for errors in the forward model due to emissivity errors
and undetected cloud/precipitation. We developed the new observation errors and ran assimilation trials using
these new situation-dependent values. We also investigated extending the coverage with these new observation
errors by relaxing screening over high orography and by relaxing the cloud screening. First results showed that
the new observation errors had a neutral impact on forecast scores when no new data were added but there was a
reduction in the standard deviation of background departures for ATMS when the AMSU-A cloud screening was
relaxed, which was encouraging.
1
Introduction
At ECMWF, radiances from AMSU-A temperature sounding channels are actively assimilated from
instruments aboard 6 different polar-orbiting satellites, providing a very good global coverage. The
tropospheric channels are particularly important for weather prediction but they suffer from cloud contamination and uncertainties in surface temperature and emissivity since they are surface-sensitive, and
this will produce errors in the forward model. When assimilating the radiances of these channels we
must define observation errors, which should include this forward model error as well as the instrument
noise. Currently, fixed values of 0.28 K and 0.20 K are applied for channels 5 and 6 - 7 respectively.
Here we present a method for calculating situation - dependent observation errors which depend on the
surface temperature, surface-to-space transmittance and liquid water path. The approach follows methods outlined by [Candy, 2010], [Lean et al., 2012], [Di Tomaso et al., 2013] but includes a non-constant
liquid water path error. First results from assimilation trials using these observation errors are also
shown.
2
Situation Dependent Observation Errors
The total observation error, σo , for the lower peaking channels of AMSU-A can be written as a summation of the instrument noise, σN , and the forward model errors which for surface- and cloud-sensitive
channels includes a surface term, σsur f ace , and a liquid water path (lwp) term. Thus σo can be expressed
as follows:
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2
2
2
σo2 = σsur
f ace + σlwp + σN
AMSU-A
(1)
The σlwp -term arises as we currently assimilate AMSU-A using a clear-sky radiative transfer model.
To limit the effect of cloud contamination, clear-sky observations are identified in the ECMWF system
in the following way: the absolute value of FG-departures in a window channel needs to be below a
certain threshold (using channel 3 and a threshold of 3 K over ocean, and channel 4 and a threshold
of 0.7 K over land), and an observation-based estimate of the lwp needs to be below 0.3 kg/m2 over
oceans. Attempts at using the tropospheric AMSU-A channels in all-sky conditions have so far not been
successful [Geer et al., 2012].
The surface and lwp terms of (1) were calculated as follows.
2.1
Surface Errors
Currently the land and sea-ice surface emissivities used for AMSU-A sounding channels are retrieved
prior to the assimilation from the radiances of a window channel (channel 3), following the method
developed by [Karbou et al., 2006]. Sea surface emissivities are calculated from the FASTEM model.
The forward model error due to emissivity errors, σsur f ace , can be approximated to ([English, 2008]):
σsur f ace ≈ TS τ 2 σε ,
(2)
where TS is the skin temperature, τ is the surface-to-space transmittance and σε is the surface emissivity
error. Note that in (2) we assume an isothermal atmosphere and that the atmospheric temperature may
be approximated to the skin temperature, Ts . We do not consider contributions from errors in the skin
temperature because, in the ECMWF 4D-Var assimilation system, the skin temperature is retrieved
during the analysis as a sink variable.
For cloud-free data (1) can therefore be rewritten as:
σo2 ≈ TS τ 2 σε
2
+ σN2 ,
(3)
The emissivity errors, σε , were estimated for different surface types by fitting (3) to the mean-square
2
background departures as a function of binned first guess Ts τ 2 values for channel 5 AMSU-A. This
was done for all data which had been filtered for cloud-contamination. Cloudy data were identified using
the standard IFS quality control, with a tighter check on clouds over ocean excluding data with lwp >
0.05 kg/m2 . Noise terms, σN , were simultaneously calculated as the intercept. Values were obtained for
σε for ocean, sea-ice, snow-covered land and snow-free land and these are given in table 1. Previously
[Di Tomaso et al., 2013] calculated values for different land surface types (forest, desert, etc.) but, with
the exception of snow cover, these values were all very similar. We therefore decided to combine the
land surfaces into two types only: snow-free and snow-covered.
Table 1: Emissivity errors for different surface types
Surface Type
Ocean
Snow - free land
Snow - covered land
Sea-ice
2
σε
0.015
0.022
0.050
0.050
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We checked the validity of values found for σε for different surface types by calculating also the standard
deviation of retrieved emissivities for these surfaces. This produced similar to values to those shown in
table 1.
2.2 Liquid Water Path Errors
Errors arising from neglecting cloud-contributions in the radiative transfer are parameterised empirically
using an estimate of the liquid water path in the observations. The liquid water path is calculated over
ocean from AMSU-A window channels 1 and 2, following the method of [Grody et al., 2001]. The
standard deviation of background departures gives us a good indication of the observation errors for
AMSU-A channels 5 - 7 and so we can look at how they vary with liquid water path (over ocean). Figure
1 shows that the standard deviation of background departures increases approximately quadratically for
channels 5 and 6 and in a linear manner for channel 7. We therefore decided to model the liquid water
path error terms as follows:
channels 5 and 6:
σlwp = Alwp2 + Blwp,
(4)
σlwp = Alwp,
(5)
channel 7:
for some constants A and B. We can thus rewrite the observation error due to instrument noise and liquid
water path terms as:
channels 5 and 6:
2
σo2 = σN2 + Alwp2 + Blwp
(6)
σo2 = σN2 + (Alwp)2
(7)
channel 7:
Applying a quadratic fit has some physical basis, since the cloud liquid water will affect the τ term
(surface-to-space transmittance) in the radiative transfer equations, which takes the form of an exponential. The additional exponential term could be approximated to a quadratic in a Taylor expansion.
However it is worth noting that the first guess departures are also affected by scattering of ice clouds,
snow and rain which are likely to be correlated to some extent to cloud liquid water. Some of the dependency of first guess departures on the cloud liquid water path may be due to this correlation to scattering,
and this correlation may even dominate over cloud liquid water effects particularly for channels 6 and 7.
Assuming that the observation errors are dominated by liquid water path errors over ocean, we calculated
a best fit of (6) and (7) where the standard deviation of background departures were used as a proxy for
σo , in order to obtain values for constants A, B and σN . We found the following best fits for σlwp , which
are also plotted in figure 1 for an instrument noise of 0.25 K for channel 5 and 0.20 K for channels 6
and 7:
channel 5:
σlwp = 0.2lwp2 + 0.79lwp,
(8)
σlwp = 0.54lwp2 + 0.30lwp,
(9)
σlwp = 0.20lwp.
(10)
channel 6:
channel 7:
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Model
lwp data screen
Channel 5 data
Channel 6 data
Channel 7 data
0.6
0.5
stdev(o−b)
OBSERVATION ERRORS FOR
0.4
0.3
0.2
0.1
0
0.05
0.1
0.15
0.2
0.25
lwp (kg/m2)
0.3
0.35
0.4
Figure 1: Standard deviation of background departures as a function of binned liquid water path
values for channels 5, 6 and 7 of AMSU-A. The different points indicate different satellites. The red
lines show the best fits and the black dashed line indicates the liquid water path value above which
data are not used for channels 5 or 6.
Note that over land we currently do not attempt to model the error contribution from neglecting cloud
effects in the observation operator.
2.3
Instrument noise
When calculating the best fits for the surface and liquid water path errors we simultaneously calculated
noise terms for each satellite instrument (in sections 2.1 and 2.2), as the intercept values. These varied
for different satellite-channel combinations but it was decided to keep a constant value for each satellite.
A fixed value of 0.25 K was used for channel 5 instrument noise term, σN , and 0.20 K for channels 6
and 7. These values are the highest found for the satellite-channel combinations.
3
First assimilation trials
Situation-dependent observation errors allow us to weight the data in a more accurate manner. This also
means that they may allow us to introduce more data over areas which are currently excluded from the
assimilation, as they showed higher forward model errors that were previously not accounted for. This
includes areas with high orography, the South Pole or areas with weak cloud-contamination.
The following experiments were run:
• Control: The operational 4D-VAR model (version 40R1) at T511 with 137 vertical levels, including some contributions to cycle 40R2. Observation errors for AMSU-A channels 5 - 7 are
constant.
• Situation-dependent observation errors: The same as the control with observation errors changed
to (1) combined with (2) and (8) - (10) for channels 5 - 7.
• Extended coverage over cloudy regions: The same as Situation-dependent observation errors with
the window channel background departure check removed over ocean and replaced by a scatter
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index check (keeping data with scatter index < -30K). As with the control, data are also not used
for channels 5 and 6 if the liquid water path exceeds 0.3 kg/m2 .
• Extended coverage over high orography: The same as Situation-dependent observation errors with
channel 5 coverage extended over sea-ice in the Southern Hemisphere (it is currently blacklisted
operationally) and data for channels 5 - 7 introduced over high orography. Instead, we reject data
with observation errors larger than 0.35 for channel 5 and 0.28 for channel 6 (2 x the noise).
Each experiment was performed over 2 months for the period 15 June 2013 - 14 August 2013.
4
Results
The new observation errors down-weight data with a higher liquid water path, a higher surface-to-space
transmittance and/or a higher surface temperature. Equally data with a lower liquid water path, or
surface sensitivity have more weight. Figure 2 shows the new observation errors for channel 5 for the
‘Situation dependent observation errors’ experiment. In this figure we can see that for channel 5 the
observation errors are higher in the centre of the swath, where the observation angle is close to nadir
and surface-to-space transmittance is higher. There are also higher values over sea-ice due to a higher
emissivity error and higher values in areas of high liquid water path which pass the cloud-screening,
such as over the Southern hemisphere ocean. Note that in the tropics data with high liquid water paths
generally do not pass the current cloud screening.
0.48
0.35
60°N
0.34
0.33
30°N
0.32
0.31
0°N
0.30
0.29
30°S
0.28
0.27
60°S
0.26
0.25
150°W 120°W 90°W 60°W 30°W
0°E
30°E
60°E
90°E 120°E 150°E
Figure 2: Observation errors for Metop-B AMSU-A channel 5 for 15 June 2013. The edges of
the scanline have lower observation errors due to lower surface-to-space transmittance. Higher
observation errors over land, sea-ice and high liquid water path can also be seen.
The extended coverage experiments used more data, as shown in figure 3:
Results of the experiments with the new situation-dependent observation errors indicated a generally
neutral impact on globally averaged forecast scores. For example the forecast scores for 500hPa geopotential height are shown in figure 4.
Extending the coverage by relaxing the cloud-screening produced a mainly neutral impact on forecast
scores (see figure 4) but reduced the standard deviation of background departures for ATMS, as shown
in figure 5. This latter result is encouraging since ATMS data are strongly screened for cloud and so the
new AMSU-A data are in agreement with the non-cloudy ATMS data.
Extending the coverage over high orography changed the mean forecast fields over the South Pole and
Greenland, and the forecast impact over Antarctica is mainly negative. The positive scores below 500hPa
shown in figure 6 are deceptive because the land is higher than this over Antarctica and so these scores
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a)
50
39
35
31
27
23
19
15
11
7
3
0
0
-3
-7
-11
-15
-19
-23
-27
-31
-35
-39
60°N
30°N
0°N
30°S
60°S
150°W 120°W 90°W
60°W
30°W
0°E
30°E
60°E
90°E
120°E 150°E
b)
166
118
106
94
82
70
59
47
35
23
11
0
0
-11
-23
-35
-47
-59
-70
-82
-94
-106
-118
60°N
30°N
0°N
30°S
60°S
150°W 120°W 90°W
60°W
30°W
0°E
30°E
60°E
90°E
120°E 150°E
Figure 3: Change in the number of data used for MetOp-B AMSU-A channel 5 (1 month average)
between a) Extended coverage over cloudy regions experiment and control and b) Extended coverage
over high orography and control
a) Z: −90° to −20°, 500hPa
Normalised difference
0.06
b) Z: 20° to 90°, 500hPa
0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
−0.04
−0.04
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Situation-dependent observations errors – Control
Extended coverage cloud – Control
Extended coverage orography – Control
Figure 4: Normalised difference in the root mean square forecast error for 500 hPa geopotential
as a function of forecast day (x axis). Values are averaged for 2 months over a) Northern hemisphere extra-tropics and b) Southern hemisphere extra-tropics. Error bars indicate 95 % confidence
intervals.
do not have meaning. More work is required to attribute the impact to either the introduction of data
over Antarctica or over the sea-ice. Elsewhere, the use of the additional data leads to a neutral to slightly
positive impact on forecast scores in the Northern hemisphere, as shown in figure 6. This is encouraging
as it may suggest improvements due to the less restricted orography screening in these areas.
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b)
22
20
Channel number
18
14
12
10
8
6
99.2
99.4 99.6 99.8 100 100.2 100.4
Analysis std. dev. (%, normalised)
99.2
99.4 99.6 99.8 100 100.2 100.4
FG std. dev. (%, normalised)
Figure 5: Standard deviation of a) analysis departures and b) background departures for the ATMS
instrument (averaged globally) of the Extended coverage over cloudy regions normalised by the
values of the control experiment.
b)
T+72
200
Pressure, hPa
Pressure, hPa
a)
400
600
800
1000
−90 −60 −30 0
30
Latitude
−0.10
60
90
T+72
200
400
600
800
1000
−90 −60 −30 0
30
Latitude
0
0.05
−0.05
Difference in RMS error normalised by RMS error of control
60
90
0.10
Figure 6: Change in the root mean square day 3 geopotential (left) and temperature forecasts (right)
minus analysis between the extended coverage over orography experiment and control as a function
of latitude (x axis) and pressure (y axis). Blue indicates a reduction in day 3 forecast error and red
an increase.
5
Conclusions
New situation-dependent observation errors were calculated for AMSU-A channels 5 - 7 and these were
tested in assimilation trials lasting 2 months. The new observation errors appeared to show neutral
impact when the same cloud and orography screening was used. However when the cloud screening
was relaxed the standard deviation of background departures was reduced for ATMS, indicating that the
new data used for AMSU-A reinforced the ATMS data which is strongly screened for cloud. This is
encouraging. Introducing new data by relaxing the orography screening led to mainly neutral results but
with some small improvement in the geopotential forecast over the Northern Hemisphere.
Further experimentaton over longer periods and different seasons is required to corroborate our findings.
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Acknowledgements
Heather Lawrence is funded by the EUMETSAT fellowship programme. Anabel Bowen is gratefully
acknowledged for her help editing the figures.
References
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